Related papers: Some probability inequalities for multivariate gam…
We study distributions of differences of unscaled Riemann zeta zeros, $\gamma-\gamma'$, at large. We show, that independently of the location of the zeros, their differences have similar statistical properties. The distributions of…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
In this paper, we investigate the complete monotonicity of some functions involving gamma function. Using the monotonic properties of these functions, we derived some inequalities involving gamma and beta functions. Such inequalities…
Using Malliavin operators together with an interpolation technique inspired by Arratia, Goldstein and Gordon (1989), we prove a new inequality on the Poisson space, allowing one to measure the distance between the laws of a general random…
Gaussian distributions can be generalized from Euclidean space to a wide class of Riemannian manifolds. Gaussian distributions on manifolds are harder to make use of in applications since the normalisation factors, which we will refer to as…
We perform a covariant constraint analysis of massive gravity valid for its entire parameter space, demonstrating that the model generically propagates five degrees of freedom; this is also verified by a new and streamlined Hamiltonian…
We consider random graphs with a given degree sequence and show, under weak technical conditions, asymptotic normality of the number of components isomorphic to a given tree, first for the random multigraph given by the configuration model…
To most applied statisticians, a fitting procedure's degrees of freedom is synonymous with its model complexity, or its capacity for overfitting to data. In particular, it is often used to parameterize the bias-variance tradeoff in model…
In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…
We discuss several limiting degree distributions for a class of random threshold graphs in the many node regime. This analysis is carried out under a weak assumption on the distribution of the underlying fitness variable. This assumption,…
We consider covariance estimation in the multivariate generalized Gaussian distribution (MGGD) and elliptically symmetric (ES) distribution. The maximum likelihood optimization associated with this problem is non-convex, yet it has been…
The central limit theorem provides the theoretical foundation for the universality of the normal distribution: under broad conditions, the asymptotic distribution of a sum of independent random variables approaches a Gaussian. Yet, physical…
We study the asymptotic zero distribution of type II multiple orthogonal polynomials associated with two Macdonald functions (modified Bessel functions of the second kind). Based on the four-term recurrence relation, it is shown that, after…
In this expository and survey paper, along one of main lines of bounding the ratio of two gamma functions, we look back and analyse some inequalities, the complete monotonicity of several functions involving ratios of two gamma or $q$-gamma…
The standard central limit theorem with a Gaussian attractor for the sum of independent random variables may lose its validity in presence of strong correlations between the added random contributions. Here, we study this problem for…
Unlike classical and free independence, the boolean and monotone notions of independence lack of the property of independent constants. In the scalar case, this leads to restrictions for the central limit theorems, as observed by F.…
This paper introduces the notion of probabilistic zero bounds for random polynomials. It presents new results regarding the probabilistic bounds of random polynomials whose coefficients are independently and identically distributed as…
Pearson's is the most common correlation statistic, used mainly in parametric settings. Most common among nonparametric correlation statistics are Spearman's and Kendall's. We show that for bivariate normal i.i.d. samples the pairwise…
For interacting classical field theories such as general relativity exact solutions typically can only be found by imposing physically motivated (Killing) {\it symmetry} assumptions. Such highly symmetric solutions are then often used as…
Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the…